Coontents

group theory

# Coontents

## Definition

The rank of a Lie group is the dimension of any one of its Cartan subgroups, hence equivalently the dimension of any one of the Cartan subalgebras of its Lie algebra.

## Properties

### For compact connected Lie groups

For connected compact Lie groups then a Cartan subgroup is a maximal torus and hence in this case the rank of the Lie group is the dimension of any one of its maximal tori.

## References

Created on January 10, 2017 at 11:08:56. See the history of this page for a list of all contributions to it.